Strings that are not substrings but are subsequences...WHAT?!

Here we look at the language of all strings within a regular language L that, given a finite language L', (1) no string in L contains a substring that is a string in L', and (2) for each string in L', it is a sub*sequence* of a string in L. The goal is to show the resulting language is regular.

Yes, I know it sounds complicated, but the idea is very simple. We just show that (1) and (2) are regular, and then the result is regular. For both we make regular expressions that allow us to conclude that each is regular. Because L' is finite, even though (2) seems more complicated, it is very easy to make a regular expression for it.

▶ADDITIONAL QUESTIONS◀
1. What if L' were infinite?
2. What if we wanted the strings that are either in (1) or (2), but not both?

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I am a professor of Computer Science, and am passionate about CS theory. I have taught over 12 courses at Arizona State University, as well as Colgate University, including several sections of undergraduate theory.

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[real-investment-banker]

Not able to get the explanation of (1)

We needed such string in L' such that no string of this language is a substring of any w (that belongs to) L

First what we did, is that we made another language let us call it P. Here we included those strings which are a substring of any w that belongs to L. Right?

Now we can form a language that will include strings in P as a substring, let's call this Q. By using regex and concatenation.

And taking a complement of this Q, will get us all this strings which do not include where any string of P acts a substring in Q. But here you wrote that "all strings in sigma* that contain something in L' as a substring", wouldn't this be opposite?

Or, I'm just moving to the wrong direction and interpreted it all wrong